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What is the domain of #f(x)=secx#?

Answer 1

Sophie Adams

By rewriting a bit,

#f(x)=secx=1/cosx#.

Since the denominator cannot be zero, we need to exclude numbers that make #cosx# equal to zero.

Since for all integer #n#,

#cos(pi/2+npi)=cos({2n+1}/2pi)=0#,

the domain of #f# is all real numbers except for #x={2n+1}/2pi# for all integer #n#.

I hope that this was helpful.

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Answer 2

Anna Allen

The domain of ( f(x) = \sec(x) ) is all real numbers except where ( \cos(x) = 0 ), because division by zero is undefined. Therefore, the domain is ( x ) such that ( x \neq (2n + 1)\frac{\pi}{2} ), where ( n ) is an integer.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.